Cluster-glass state in manganites induced by A-site cation-size disorder

Cluster-glass state in manganites induced by A-site cation-size disorder

K. F. Wang, Y. Wang, L. F. Wang, and S. Dong

Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China

D. Li and Z. D. Zhang

Shenyang National Laboratory for Material Science, Institute of Metal Research and International Center for Materials Physics, Chinese Academy of Sciences, Shenyang 110016, China

H. Yu, Q. C. Li, and J.-M. Liu*

Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China and International Center for Materials Physics, Chinese Academy of Sciences, Shenyang 110016, China

共Received 12 September 2005; revised manuscript received 15 December 2005; published 11 April 2006兲

The dependence of magnetotransport behaviors onA-site disorder induced byA-site cational size mismatch in ferromagnetic manganites is investigated by characterizing a series of samples with the sameA-site cational mean radius 具r_A典= 1.20 Å but differentA-site ionic radii variance ␴²=兺ix_ir_i²−具r_A典², wherex_iand r_iare the atomic fraction and ionic radii ofi-type ions atA-site, respectively. It is revealed that the ground state transits from ferromagnetic metal to cluster-glass insulator upon increasing the variance ␴² from 0.0003 for La_0.55Ca_0.45MnO₃ to 0.015 for Sm_0.55共Ca_0.6Ba_0.4兲0.45MnO₃, while the crystallographic structure and lattice constants of these manganites remain unchanged. Nevertheless, the increasing A-site disorder is believed to enhance the random local radial distortion of MnO₆ octahedra and suppress the ferromagnetic long-range order. In the manganites of highA-site disorder, the long-range ferromagnetic ordering is completely melted into the short-range magnetically ordered clusters and then the stepwise magnetization. With decreasing tem- perature, the short-range ordered clusters become frustrated at the frustrating point, below which a cluster-glass transition occurs due to the weak intercluster interaction.

DOI:10.1103/PhysRevB.73.134411 PACS number共s兲: 75.30.Kz, 71.30.⫹h, 75.40.Cx

I. INTRODUCTION

Perovskite manganites, whose resistivity can change on the order of 10⁴– 10⁶ by applying external magnetic fieldH of a few tesla, continue attracting the attention of condensed matter physicists.^1–3This colossal magnetoresistance共CMR兲 effect can be qualitatively understood in the framework of the double-exchange interaction model共DE兲.⁴When the rare earth site共A-site兲is doped with a divalent ion, a proportional number of Mn³⁺ ions are converted into Mn⁴⁺ ions and mobileeg electrons are introduced, mediating the ferromag- netic共FM兲interaction between Mn³⁺and Mn⁴⁺ according to the DE interaction. In these manganite systems, the hopping of eg electrons between two partially filled d orbitals of neighboring Mn³⁺ and Mn⁴⁺ ions via the orbital overlap eg-O2p_␴-eg, and the strong Hund coupling between thet_2g core spins and the mobile eg electrons’ spins cause the FM interaction between Mn³⁺ and Mn⁴⁺.

However, recently it has been recognized that the phase diagram of manganites and many other strong correlated electron systems is multicritical, involving competing spin, charge, or orbital, and lattice orders.⁵ The competition be- tween these interactions and/or orders inherent in mangan- ites, such as between double-exchange ferromagnetism and superexchange antiferromagnetism 共AFM兲 and between charge-orbital ordered共CO-OO兲state and metallic state, will produce the multicritical state.⁶In relation to the competition between the CO-OO state and FM metallic state共FMM兲, a scenario of the electronic phase separation has arisen as a generic feature of manganites. It has been accepted that,

given a temperature T and magnetic field H, the electronic and magnetic ground state of manganites can be inhomoge- neous due to the coexistence of FMM phase and CO-AF insulating共AFI兲phase. The coexisting two phases originate from the electronic phase separation.^2,7,8

On the other hand, the importance of the intrinsic disorder in the strong correlated mix-valence systems was recognized.

The research on Ln_0.5Ba_0.5MnO₃, where Ln and Ba ions can form either an ordered or a disordered structure, reveals the significant disordered effects in manganties.⁹ In the ordered phase or “clean limit,” where Ln and Ba ions form a periodic layered structure, the phase diagram shows a multicritical behavior where FMM and CO-OO state compete with each other. For the disordered case, where the arrangement of共Ln, Ba兲 ions is completely random, the diagram changes in a very asymmetric manner: FMM phase is partially suppressed but still survives at finite temperature, while the CO-OO state disappears and instead some glassylike state is realized at low temperature. The enhanced CMR effect is observed in the region where the disorder induces the transition from CO-OO to FMM. Earlier research revealed that the site dis- order not only produces the glassy state but also enhances the fluctuation of the competition orders, i.e., between the CO-OO and FMM states, near the original bicritical point.^10–15Such a large fluctuation is amenable to an external field favoring the FMM phase and may be one of the most essential ingredients of the CMR physics. In fact, the disor- der introduced by Mn-site doping was studied carefully. The Cr doping on Mn site gives rise to the FM clusters coexisting with the CO-OO background.^14,15The doping with the non-

magnetic Ga ions makes the first-order transition in La_2/3Ca_1/3MnO₃continuous,¹¹and the long-range FM phase coexists with short-range magnetic correlations in the low doping level.¹² So, the first-order transition in pure La_2/3Ca_1/3MnO₃ is induced by fluctuations from competition.¹¹Theoretical approaches also predicted that the disorder in the critical region may produce phase coexistence of two competing ordered phases on various time and length scales.^16–18

In addition to theB-site doping and Ba-based manganites, theA-site cation size disorder can also be interesting. Here- after, theA-site cation size disorder共in short, theA-site dis- order兲 is designated to the disorder induced by A-site ionic radii mismatch. It has been proven that the variance of the A-site ionic radii,␴²⁼兺ixir_i²−具rA典², where xi andri are the atomic fraction and ionic radii of i-type ions at A-site, re- spectively, govern the magnetic and transport properties of manganites, and thus can be defined as the parameter to char- acterize theA-site disorder. In fact, earlier works often took the tolerance factort=共具rA典+rO兲/

冑

^2共rMn+r_O兲as a parameter to interpret the relationship between the magnetotransport behaviors and lattice structure of manganites. Although this tolerance factor is related to the A-site cation mean radius 具rA典, noA-site disorder is taken into account.^19–21It was also reported that the temperatureTmof the transition from FMM to paramagnetic 共PM兲 insulator varies as Tm=Tm共0兲−pQ² due to the strain fields resulting from ordered or disordered oxygen displacementsQthat are parametrized by the statis- tical mean and variance of theA-cation radius, respectively.¹⁹ In this case, the effect of theA-site disorder on the transition temperatureTmis explained.

Compared with the Mn-site doping, the A-site cational size mismatch can introduce the disorder over a wide range and then the local lattice distortion can be modulated to a large extent. But, this mismatch does not cause significant change of the crystallographic structure and lattice constants, in the sense of x-ray diffraction共XRD兲over a macroscopic volume of sample. Neither magnetic impurity nor change of the Mn³⁺/ Mn⁴⁺ratio will be possible. Therefore, a study on theA-site disorder may be a more direct and purified road- map to understand the physical mechanism associated with disorder in manganites. One may expect that theA-site dis- order can lead to the same effects as by the Mn-site disorder, such as cluster-glass behavior and phase-separated state.

As mentioned above, the effects of theA-site disorder in manganites were previously investigated.^19,20However, pre-

vious studies only pointed out the relevance betweenTmand the A-site disorder; not much data on phase separation be- haviors associated with the A-site disorder are available so far. In particular, to the authors’ best knowledge, no experi- mental evidence on the cluster-glass ground state at low tem- perature as induced by theA-site disorder has been reported.

It is expected that theA-site disorder may not only suppress the ferromagnetic transition but also prefer the localization of electrons. In this paper, the effect ofA-site disorder over a broad range in ferromagnetic manganites will be investigated by preparing a series of samples which have the sameA-site cation mean radius具rA典= 1.20 Å but different values of vari- ance␴²ranging from 0.0003 to 0.015 Ų. One of the experi- mental findings is that a destabilization of the FM metal ground state is indeed possible by mediating the A-site disorder.²²We shall present in this work detailed experimen- tal evidence on the transitions of the ground state from FM metal to low-temperature spin cluster-glass insulator in man- ganites with highA-site disorder.

This paper is organized as follow. We report the sample preparation and property characterizations using various techniques in Sec. II. The multifacet experimental evidence and discussions on the low-temperature cluster-glass state induced by theA-site disorder will be presented in Sec. III, followed by a conclusion in Sec. IV.

II. EXPERIMENTAL PROCEDURES

A series of samples which have a constantA-site cation mean radius具rA典= 1.20 Å but different values of variance␴² as shown in Table I was chosen for the present study. The values of radius and variance␴²were calculated using stan- dard nine-coordinated cation radii.²³All the ceramic samples were prepared by the conventional solid-state reaction in air.

The highly purified powders of oxides-carbonates were mixed in stoichiometric ratios, ground, and then fired at 1250 ° C for 24 h in air. The resultant powders were re- ground and pelletized under 3000 psi pressure to disks of 1 cm in diameter; then, the pellets were sintered at 1400 ° C in air for 12 h.

In order to check whether our samples have the same A-site cational mean radii and then the same lattice param- eters, high-resolution XRD with CuK␣ radiation at room temperature on these samples was performed, assisted by careful lattice structure characterization using the Rietveld refining method.

TABLE I. Summary of chemical, structural and physical data for theRE_0.55AE_0.45MnO₃series with a constantA-site cation mean radius具r_A典= 1.20 Å.

Composition ␴²共Ų兲 T_MI共K兲 T_C共K兲 T_f共K兲

M共T= 3 K兲 共␮Bper formula unit兲

La_0.55Ca_0.45MnO₃ 0.0003 228.7 232.6 3.48

Nd_0.55共Ca_0.45Sr_0.55兲0.45MnO₃ 0.003 200.8 194.5 3.36 Sm_0.55共Ca_0.2Sr_0.8兲0.45MnO₃ 0.007 105.7 115.5 2.82

Nd_0.55共Ca_0.76Ba_0.24兲0.45MnO₃ 0.008 42.0 2.62

Gd_0.55Sr_0.45MnO₃ 0.009 42.0 1.51

Sm_0.55共Ca_0.6Ba_0.4兲0.45MnO₃ 0.015 42.5 1.01

The effects of the A-site disorder on the transport and magnetization of all the samples were studied carefully. The transport measurements were performed using a standard four-probe method down to 20 K under zero field and a mag- netic fieldH= 6 T using a MPMS共magnetic properties mea- surement system兲. The magnetic property including the ac susceptibility as a function of temperatureT andHwas also measured using a Quantum Design SQUID共superconducting quantum interfering device兲. In the zero-field cooled 共ZFC兲 measurements the samples were cooled from ⬃300 to 3 K under zero field, and then the ZFC magnetization measure- ments were performed in the warming process with a field of H= 100 Oe. For the field-cooled 共FC兲 cases, the samples were first cooled to 3 K in the presence ofH= 100 Oe; then, the magnetization was probed under the same field during the heating cycle. The magnetic loops were recorded at 3 K fromH= 0 to 7 T after the ZFC sequence.

III. RESULTS AND DISCUSSION A. Crystal structure

In Fig. 1共a兲we present the XRD␪-2␪ patterns measured at room temperature for a set of samples with different val- ues of variance␴²共A: 0.003,B: 0.007,C: 0.008,D: 0.009,E:

0.015兲. The unit of␴^{2is Å2}hereafter unless stated otherwise.

All the samples are well crystallized with pure orthorhombic structure with space groupPbnm. No identifiable reflection shift upon increasing variance␴²is observed, which demon- strates no change of the crystallographic structure and lattice constants on variance␴². To confirm this effect, we perform the Rietveld refinement²³on the diffraction spectra. The data on two samples 共␴²= 0.007 and 0.009兲 are shown in Figs.

1共b兲and 1共c兲, where the open circle dots represent the mea- sured XRD reflections and the solid lines are the Rietveld refined results. Very small difference is shown between the measured spectra and refined ones. The reliability of the Rietveld refinement is demonstrated by the high-quality re- finement parameters Rp= 11.3%, Rwp= 12.4%, and S= 1.19 for the sample of ␴²= 0.007, and Rp= 10.8%, Rwp= 16.4%, andS= 1.19 for the sample of␴²= 0.009. The lattice param- eters at room temperature as obtained by the refinement are a= 5.4831共5兲Å, b= 5.4706共3兲Å, c= 7.7283共6兲Å for the sample of␴²= 0.007. For the sample of␴²= 0.009, they are a= 5.4763共7兲Å, b= 5.4682共6兲A, c= 7.7266共3兲Å. It is re- vealed that the volume change associated with the variation of␴² from 0.0003 to 0.015 is less than 0.5%.

The argument that the crystallographic structure is inde- pendent of variance of␴²is based on the XRD data averaged over a macroscopic volume of the samples. It does not mean that no local lattice distortion occurs due to different ␴^2. However, the distortion of local lattices is spatially random over the whole sample, resulting in the invariance of the XRD-probed lattice structure in the macroscopically aver- aged sense. We shall return to this issue below, and will see that the influence of theA-site disorder on the local structure distortion can be significant, as characterized by the tremen- dous change of the transport and magnetic properties.

It is therefore concluded that, given the constant A-site cation mean radius具rA典= 1.20 Å, the variation of the A-site

disorder as characterized by variance␴²causes no change of the crystal structure. The lattice parameters remain nearly unchanged as well.

B. Metal-insulator transition

We measured the zero-field resistivity␳as a function ofT for all samples over theT range from 20 to 300 K; the re- sults are shown in Fig. 2共a兲. An overall comparison of the data demonstrates the significant effect of theA-site disorder on the transport behaviors. In general, one sees an overall increasing of ␳ with increasing ␴². For the sample La_0.55Ca_0.45MnO₃ 共␴^{2= 0.0003}兲, the T dependence of ␳ ^ex- hibits the typical insulating behavior in the high-Trange. The resistivity ␳ reaches the maximum at T=TMI= 228.7 K and decreases with further decreasing of T, where TMI is the metal-insulator transition共MIT兲 point, noting that the mea- sured T_MIis in agreement with earlier reported data.² Simi- larly, the samples Nd_0.55共Ca0.45Sr_0.55兲0.45MnO₃ 共␴²= 0.003兲 FIG. 1.共Color online兲 共a兲X-ray diffraction␪-2␪spectra at room temperature for a series of samples of variance␴²共from bottom to top兲:共A兲0.003;共B兲0.007;共C兲0.008;共D兲0.009; and共E兲0.015.共b兲 Measured XRD ␪-2␪ spectrum 共open circle dot, measured兲 and evaluated spectrum 共solid line, Rietveld refined兲 using Rietveld structural refinement for sample of ␴²= 0.007. 共c兲 Measured and Rietveld refined spectra for sample of ␴²= 0.009. The difference 共dashed line, difference兲 between the measured and Rietvield re- fined spectra for the two samples, respectively, is plotted with a slightly downshift for clarity in共b兲and共c兲. The unit of␴²is Ų.

and Sm_0.55共Ca_0.2Sr_0.8兲0.45MnO₃ 共␴^{2= 0.007}兲 again show the MIT behavior, with T_MI decreasing from 201 to 106 K, as shown in Fig. 2共b兲, where the uncertainties forTMIare also inserted. Referring to sample Nd_0.55共Ca0.76Ba_0.24兲0.45MnO₃ for which ␴²= 0.008, no MIT behavior can be observed and the insulator ground state is kept over the whole T range. Further increasing ␴² only causes the increase of

␳^{. The samples Gd}0.55Sr_0.45MnO₃ 共␴²= 0.009兲 and Sm_0.55共Ca0.6Ba_0.4兲0.45MnO₃ 共␴²= 0.015兲 remain insulating over the wholeT range too.

The significantly different transport behavior upon differ- ent values of ␴² as shown above allows us to argue the essential role of theA-site disorder in mediating the phase separation of ferromagnetic manganites, noting that no charge-ordered phase appears upon increasing theA-site dis- order. Therefore, we turn to the magnetic behaviors of these samples in order to reveal the magnetic ground state in the manganites of differentA-site disorder degrees.

C. Magnetization behavior

Figure 3 shows theTdependence of the dc magnetization M for samples of ␴²= 0.0003, 0.007, 0.008, 0.015. The samples with small A-site disorder degree 共␴²= 0.0003 and 0.007兲 exhibit a PM-FM transition at T_m= 232.6 and 122.9 K, respectively共Tmwas determined using the Lorent- zian function fit of the derivation curves兲. Increasing ␴² causes a decrease of Tm, which is in accordance with the MIT transition point shown in Fig. 2共b兲. As ␴² further in- creases, theM-Tcurves at ZFC cases show a cusplike peak

at about T=Tf⬃42 K when ␴² is higher than 0.008. This effect immediately allows us to argue a possible spin-glass- like transition occurring at T_f. In fact, similar peaks were observed at the cluster-glass transition for La_2/3Ca_1/3MnO₃ with Ga, Al, and Fe doping at the Mn site, respectively.^12,24,25 Notice that for all the samples there appears an irreversibility between the ZFC and FC magnetization curves. However, this irreversibility is very small at small␴², even at tempera- ture below the cusplike peak. It becomes remarkable for the samples of␴²= 0.008 and 0.015 onceTis down close toTf. Such an irreversibility of the magnetization is one of the typical features of the spin-glass-like state.^26,27

TheHdependences of magnetizationM atT= 3 K for the samples of ␴²= 0.003, 0.007, 0.008, and 0.015, measured through the field-increasing and field-decreasing cycle, are shown in Fig. 4. For␴²= 0.003 and 0.007, the saturatedM is achieved at H= 1 T and higher. However, at ␴^{2= 0.008, M} remains unsaturated untilH= 3.5 T, at which a stepwise be- havior occurs. Afterwards, the magnetization becomes satu- FIG. 2.共a兲Zero-field resistivity␳as a function ofTfor all the

samples with␴²from 0.0003 to 0.015.共b兲Measured dependence of T_mon␴². The unit of␴²is Ų.

FIG. 3. Measured magnetizationMas a function ofTmeasured during warm cycle for samples of 共a兲 ␴²= 0.0003;共b兲 0.007; 共c兲 0.008;共d兲 0.015; respectively, under the ZFC and FC conditions.

The unit of␴²is Ų.

rated. Nevertheless, for the samples of␴²= 0.009 and 0.015, no saturated magnetization can be reached even at a field as high asH= 6.0 T.

It is known that the high-spin Mn gives spin-ordered mo- ment ␮=gs␮B 共orbital contribution quenched兲 where Mn³⁺

and Mn⁴⁺ carry 4␮B and 3␮B, respectively. If all Mn ions were in a FM state, the maximum spin-only ordered moment would be 3.55␮B per formula unit and the magnetic moment should remain constant 共=3.55␮B兲, because all the samples have the same Mn⁴⁺/ Mn³⁺ ratio. However, the measuredM atT= 3 K andH= 3 T is found to be 3.48, 3.36, 2.82, 2.62, 1.51, and 1.01␮B per formula unit for ␴²= 0.0003, 0.003, 0.007, 0.008, 0.009, and 0.015, respectively, as shown in Table I and Fig. 5. An abrupt decrease ofM as a function of

␴^{2 occurs at}␴²⬃0.008. As␴²= 0.015, the measuredM be- comes very small. Simultaneously, the zero-field resistivity shows an abrupt increases at␴²⬃0.008, as shown in Fig. 5.

Keeping in mind the above data on the transport and mag- netization, we can argue that the low-T ground state for the

manganites of large ␴² is neither AFM state nor FM state, excluding trace with any charge-ordered state. Instead, the spin-glass-like state becomes the ground state for these man- ganites. In order to provide further evidence for this argu- ment, we measured the ac magnetic susceptibility ␹ac as a function of T at different frequencies 共10, 100, 500, and 1000 Hz兲for all the samples. The measured results do reveal the typical features of spin-glass-like behavior at lowT for those sample of ␴²艌0.008. In Figs. 6共a兲 and 6共b兲 the data are plotted for the samples of␴²= 0.008 and 0.009, respec- tively. The peaked pattern and significant frequency- dispersion feature of the ␹ac-T curves support our above argument on the spin-glass-like state as the ground state at lowT.

The ac susceptibility data also allow us to give a rough estimate of the time scale for magnetic relaxation. From Fig.

6 we observe the peak shift toward the high temperature with increasing frequency. Given an assumption that the spin- glass follows the thermally activated relaxation, one has the relaxation time␶according to the Néel-Arrhenius law,

␶⁼␶0exp共E/kBTP兲, 共1兲 where ␻ is the driving frequency for measuring ␹ac, ␶

= 1 /␻^{, andT}P is the peak temperature. Prefactor␶0depends on the gyromagnetic precession time and is usually

⬃10⁻²⁰⁰s for typical spin-glass, although this time scale is not sound physically if one employs the Néel-Arrhenius law to estimate the value of␶0. If␶0⬃10⁻¹⁰– 10⁻¹³s, the system would be of superparamagnetism, which is composed of noninteracting magnetic particles or clusters with a temperature-dependent distribution of the relaxation times.²⁷ Our fitting results using this law, shown in Fig. 6共c兲, give an estimated value of ␶0⬃10⁻¹⁰⁰s, far shorter than the 10⁻¹⁰– 10⁻¹³s for the superparamagnetic case, but much longer than that for the typical spin glass. This indicates that the low-T ground state of our highly A-site disordered samples is not typical spin-glass but is composed of mag- netic clusters with weak intercluster interactions, i.e., the cluster-glass state. The magnetic transition for the samples FIG. 4. Measured magnetization M as a function of H at T

= 3 K for samples of共a兲 ␴²= 0.003;共b兲 0.007; 共c兲 0.008; and共d兲 0.015, respectively. The arrows indicate the cycle of H varying during measurements. The unit of␴²is Ų.

FIG. 5. ␴² dependences of magnetization M measured at T

= 3 K under a fieldH= 3 T, and zero-field resistivity␳measured at T= 50 K. The unit of␴²is Ų.

with ␴²= 0.008, 0.009, and 0.015 is essentially ascribed to the collective frustrating.²⁷

Based on all the magnetic and transport measurements presented above, we may conclude that upon increasing A-site disorder, i.e., increasing␴²from 0.0003 to 0.015, the ground state evolves from a FMM state to a cluster-glass-like insulator. This experimental finding demonstrates the essen- tial significance of theA-site disorder, similar to the B-site disorder, in modulating the ground state of manganites.

D. Disorder induced cluster-glass like transition

To understand the physics associated with theA-site dis- order, we may look back to the classical picture of mangan- ites. One of the key parameters to determine the ground state in manganites is the transfer interaction of theegstate con- duction electron between neighboring Mn sites or the effec- tive one electron bandwidth 共W兲 of the eg band. The band- widthW, which is dependent on the lattice distortion of the perovskite structure, can be described as

W= cos

冉

^{12␲−具␤典}

冊 冒

^{dMn-O3.5 , 共2兲}

where具␤典is the average angle of the Mn-O-Mn bond,d_Mn-O is the average length of the Mn-O bond which can be modu- lated by 具rA典. Since the DE interaction responsible for the FMM state is scaled byW,^28,29the stability of the FM state in a distorted perovskite manganite will be damaged, and the ground state is often replaced by competing phases against FM, such as CO-OO antiferromagnetic insulator 共AFI兲. A typical case is that a reduction of具rA典 from the ideal value will lead to ordered oxygen displacement and then a CO-OO AFI state.

However, this picture is contradictory to our experimental results. All the samples studied here have the same 具r_A典

= 1.20 Å, which is very close to the ideal value, and thus the same W. The XRD-probed crystal structure of all the samples also remains the same. Unfortunately, our experi- ments revealed that the samples with differentA-site disor- ders exhibit completely distinct properties. In fact, in MnO₆ octahedra, besides the reduction of 具rA典, the size difference between two neighboring A-site R³⁺ and M²⁺ ions around one oxygen ion can result in oxygen displacement too, and then can result in local distortion of MnO₆ octahedra or bending of the Mn-O-Mn bond in these octahedra.²⁰ In our samples, the differentA-site ions with different radii are ran- domly distributed; thus, the mode and magnitude of the MnO₆ octahedra distortions or the Mn-O-Mn bond bending are spatially random and inhomogeneous. The sample of small variance 共e.g., ␴²= 0.0003 and 0.003兲, in which the MnO₆ octahedra distortion is weak, certainly exhibits the typical properties of the large-bandwidth manganites, such as MIT accompanied by a FM-PM transition. As ␴^{2 becomes} larger, the local MnO₆ octahedra distortion becomes more serious and the number of distorted MnO₆ octahedra in- creases, i.e., theA-site disorder increases. Therefore, the Mn ions around the distorted MnO₆octahedra may no longer be able to participate in the DE process.

A direct consequence of the above effect is the decrease in Tm 共or TMI兲 with increasing variance ␴², because the local strain contribution to the transition enthalpy is suppressed.²⁰ In such case the decrease inTmis roughly linear, following T_m=T_m共0兲−pQ².²⁰The measured data presented above agree with this prediction, as shown in Fig. 2共b兲. Furthermore, be- cause of the increasing disorder, the reduction in the number of lattice sites participating in the itinerant DE interaction and then the dilution of the DE network for electron conduc- tion would suppress the system magnetization and conduc- tivity, as revealed in our experiments too.

However, it is worth noting that a dilution of the DE network may not be the only sequence of the cation disorder.

If the disorder would only produce a dilution, the FMM state should be able to survive up to much higher disorder level than what we observed above: ␴²⬃0.007. Taking into ac- count that the FM state is often replaced by CO-OO AFI in distorted manganites, the Mn ions around the distorted MnO₆ octahedra may prefer locally short-range CO-OO AFI state.

This means that the A-site disorder destablizes the long- FIG. 6. Measured ac susceptibility␹acas a function ofTat four

frequencies 共10, 100, 500, and 1000 Hz兲 for samples of 共a兲 ␴²

= 0.008 and that of共b兲␴²= 0.009, respectively.共c兲Evaluated relax- ation time␶as a function ofT_P共open dot兲and fitting curves共lines兲 using the Néel-Arrhenius law. The unit of␴²is Ų.

range FM order which maintains as ␴²⬉0.007. Once

␴²⬎0.008, the short-range magnetically ordered phase be- comes favored.

An additional evidence on the above argument is the step- wise behavior in the M-H loops for sample Nd_0.55共Ca0.76Ba_0.24兲0.45MnO₃, which has an intermediate dis- order level␴²= 0.008. The magnetization as a function ofH exhibits a sharp step atH⬃3.5 T. Such a stepwise behavior was once observed in manganites like Pr_0.55Ca_0.45MnO₃,³⁰ Prx共Ca, Ba/ Sr兲1−xMnO₃,³¹ PrxCa_1−x共Mn, Co/ Cr/ Ga兲O3,^32–34 共La, Pr/ Bi兲0.67Ca_0.33MnO₃,^35,36etc. For these manganites, the martensitic scenario based on phase separation can be used to explain the observed effect.³⁴ The FM phase which has more symmetrical perovskite domains 共i.e., with weaker orthorhombic distortion兲 can coexist with the strongly dis- torted CO-OO AFI regions.²Upon application of a magnetic field, the symmetrical perovskite domains become ferromag- netic, but the expansion of the FM phase is stopped by the interfacial strains on the boundaries between the FM and AFI regions, due to the possible strongly distorted regions on the boundaries. It is necessary forHto go beyond a critical value in order to get over the strain energy and enforce a further expansion of the FM regions. A sharp magnetization step is then observed, which is an indication of the coexistence of the long-range ordered FM regions and short-range CO-OO AFI regions in the sample with an intermediate disorder.

With further increasing of the A-site disorder, the long- range FM ground state is completely melted into the short- range magnetically ordered regions. The system can no longer develop sufficient symmetrical domains to induce the FM ordered regions. Consequently, M remains very low 共⬃1.01␮Bfor sample with ␴²= 0.015 underH= 4.0 T兲. Very similar to typical cluster-glass systems, the short-range mag- netically ordered regions in the present samples may frustrate when temperature falls to a frustrating point at which these regions begin to freeze due to the intercluster frustration. The cluster-glass transition is thus activated. Below this point, the sample exhibits a cluster-glass-like behavior in terms of the transport and magnetic properties. In short, the increasing A-site disorder makes the ground state transform from metal to insulator 共MIT兲, which occurs around ␴²⬃0.008. The long-range FM state for ␴²⬍0.007 will melt into the short-range magnetically ordered clusters as ␴²⬎0.009. At

␴²⬃0.008, the coexistence of both states is observed. This behavior seems typical for an electron localization process.

E. Transport evidence on the cluster-glass-like transition The high-temperature transport data of the samples can be used to check the above argument on the cluster-glass ground state in highlyA-site disordered manganites. TheA-site dis- order brings about the electron localization that suppresses the DE interaction. The abrupt MIT of the ground state as a function of␴²is remarkable共as shown in Fig. 5兲and mimics the typical MIT induced by the electron localization. Given the argument that theA-site disorder induces the transform of the long-range FM regions to short-range magnetically or- dered regions, one may propose that the conduction follows the variable-range-hopping共VRH兲model,³⁷

␳⁼␳i0exp关共T0/T兲^1/4兴, 共3兲 where␳i0 is the prefactor and T₀ is the characteristic tem- perature. Otherwise, the small-polaron model should be fol- lowed by the conduction,³⁸which reads

␳⁼␳0Texp共−E₀/kT兲, 共4兲 where␳0 is the prefactor, E₀ is the activation energy of the small polaron, andkis the Boltzmann constant.

Plots of ␳共T兲 data for the samples with ␴²= 0.003 and 0.007 according to both the VRH and the small-polaron model are presented in Fig. 7. For␴²= 0.003, the data agree well with the prediction of both the VRH and the small- polaron mechanism; it is impossible here to make an identi- fication of the conduction mechanism only from the transport behavior. However, the conduction for the␴²= 0.007 sample simply follows the VRH rather than the small-polaron model. Over the whole insulating T-range, a good ln␳

⬃T^−1/4 relationship is identified, whereas no satisfactory ln共␳^/T兲⬃T⁻¹ behavior is observable. The␳共T兲 data for the samples with␴²= 0.008 and 0.009 according to the VRH are shown in Fig. 8. The good linear behavior apart from the data at very low-Trange indicates that theA-site disorder is bringing about the electron localization and formation of the short-range magnetically ordered clusters.

FIG. 7. Fitting of zero-field resistivity␳as a function ofTusing the VRH model and small-polaron model for samples with共a兲␴²

= 0.003 and共b兲0.007. The unit of␴²is Ų.

F. Disorder enhanced CMR effect

In addition, it is worthy to note the CMR effect induced by the A-site disorder. Figure 9 shows the measured ␳^-T curves atH= 0 and H= 6 T, and also the evaluated magne- toresistance共MR兲ratio defined asMR=关␳共0兲−␳共H兲/␳共0兲兴as a function ofT, for the samples with␴²= 0.003, 0.007, and 0.008, respectively. We can see the sample of␴²= 0.003 ex- hibit typical CMR effects: field H induces shifting of the MIT point to higher temperature and huge decrease of the resistivity. The MR-Tcurve exhibits a peak at the MIT point.

The peaked MR ratio is⬃70% at a field ofH= 6.0 T. For the sample of␴²= 0.007, the measured MR value is⬃92% but reached at lowerT.

As␴²⬎0.008, the ground state prefers the cluster-glass- like state, as demonstrated above. Over the high-Trange, the observed MR effect is not significant. However, it is noticed that the sample in low-T range shows a fantastic effect: a field ofH= 6 T enforces the ground state to change from an insulator to a metal, and a clean MIT effect is observed under H= 6 T. The induced MR is very huge and reaches almost 100%共⬃99.9%兲 below the MIT point. This huge CMR ef- fect is obviously the outcome of the competition between the FM and AFI regions. As␴²is even larger, no MIT effect can be observed at a field of 6 T, the highest field available to us in our experiments.

G. Remarks and discussion

It is well known that the sample with the lowest A-site disorder in our experiments, La_0.55Ca_0.45MnO₃, is adjacent to the boundary between the FM phase and CO-OO AFI phase in its phase diagram.²There may exist competition between

the FM double-exchange interaction and the AFM superex- change interaction, which favor the long-range FM order and A-type AFM order, respectively. Therefore, theA-site disor- der results in a crossover from a long-range ordered state to a state with short-range ordered clusters. For the intermediate disorder case, there probably exists a Griffiths phase which can be characterized by an inhomogeneous magnetic state at the microscopic scale with coexisting clusters of the compet- ing ground states.³⁹ This Griffiths phase will appear before the system is dominated by the cluster-glass state, with in- creasing variance␴^2.

The existence of a Griffiths phase can be most directly evidenced by means of small-angle neutron scattering 共SANS兲 and nanoscale high-resolution magnetic force mi- croscopy, which are unfortunately not available to us. Here, we present indirect evidence on the Griffiths phase by ana- lyzing the susceptibility␹as a function ofTunder low mag- netic field, which could characterize the Griffiths phase.⁴⁰ Figure 10 shows the measured 1 /␹as a function ofTfor the samples with ␴²= 0.0003 and 0.007 measured under H

= 100 Oe, noting here that the ground state at ␴^{2= 0.008 is} already the cluster-glass state, as shown above. If these data follow the Curie-Weiss law, they would lie on a straight line given by 1 /␹⁼g␮^3kB共S^B_{ef f}^TC+1兲

共

T^T_C− 1

兲

^{, where Sef f} is the effective spin,g is the Lander factor,␮B is the Bohr magnetron, and T_C is the Curie point. In Fig. 10 the dashed lines are the FIG. 8. Fitting of zero-field resistivity␳as a function ofTusing

the VRH model for samples with共a兲␴²= 0.008 and共b兲0.009. The unit of␴²is Ų.

FIG. 9. Measured␳共H= 0兲and␳共H= 6 T兲as a function ofTfor samples of共a兲␴²= 0.003;共b兲␴²= 0.007; and共c兲␴²= 0.008, respec- tively. TheMRratio for each sample is plotted in the same figure.

The unit of␴²is Ų.

fitting results using this law. It is clearly shown that the high- Tbehavior of the two samples is well described by the Curie- Weiss law, and the value of TC can be determined by ex- trapolating the high-Tdata to 1 /␹= 0. We have two types of evidence to identify the existence of the Griffiths phase.

First, from the slopes of the two fitting lines, we evaluate the values ofSef fto be 8.0 and 4.0, respectively, for the samples of␴²= 0.0003 and 0.007. These values are much larger than S_{ef f}= 1.77 for an effective Mn ion共the weighted average of S_Mn4+= 3 / 2 and S_Mn3+= 2兲, indicating that the high-T para- magnetism for the two samples originates from the contribu- tions of individual magnetic entities containing more than two Mn ions, i.e., FM clusters, rather than from the contri- butions of individual magnetic ions.^39,40Second, when T is approachingT_C from the high-T side, the 1 /␹ data deviate from the Curie-Weiss fitting lines, indicating a much larger slope than the fitting line. Therefore, before the system evolves into the cluster-glass state from the FM state with increasing␴², there appears a Griffiths phase which is ran- domly distributed FM clusters atT⬎TC. Because these FM clusters have larger effective spins than individual magnetic ions, 1 /␹ as a function of T would show a large deviation from the Curie-Weiss law once the Griffiths phase appears, and can be described by a susceptibility exponent less than unity.^39,41

In the highly disordered manganites the ground state changes from a metal to an insulator. Our results reveal that the two competition interactions plus the quenched disorder

will give rise to a cluster-glass-like behavior or a phase sepa- rated state, which may be induced by the enhanced fluctua- tions between competing interactions. Moreover, such en- hanced fluctuation is amenable to an external magnetic field favoring the FMM phase, and then the huge CMR effect is observable at the intermediate disorder case. We thus argue that in the inhomogeneous states, the competition and fluc- tuations between the ordered ground states at the clean-limit case may be some of the most important ingredients of the CMR and other interesting effects in manganites.

Our results coincide with previous theoretical research and reveal the importance of disorder in manganites. Theo- retically, the disorder effects in manganites were extensively studied by Sen and Dagotto.^17,42They indicated that the ef- fect of quenched disorder on the competition between or- dered states separated by a first-order transition will produce a phase diagram with features resembling quantum critical behavior. The low-temperature region consists of coexisting ordered clusters.⁴² The disorder can induce the insulator- metal-insulator transition simultaneously.¹⁷Our experiments illustrated these features, and theA-site disorder induces the transition of the ground state from FMM to cluster-glass in- sulator, which probably is a quantum phase transition be- cause the transition is the ground state and close to 0 K.

Surely, a physically sound explanation on the observed re- sults in the present work still needs more direct evidence for the existence of short-range magnetically ordered region.

Our results indicate that the A-site disorder is an important ingredient for understanding the CMR physics and phase separation in manganites.

IV. CONCLUSIONS

In conclusion, a series of manganite compounds, with a constant averageA-site ionic radius but different variances of the A-site ionic radii ␴² from 0.0003 to 0.015, have been investigated using various experimental techniques. Our re- sults have shown that all the samples have the orthorhombic crystallographic structure and no change of lattice param- eters is observable from the XRD technique. Therefore, the lattice effects in our system are weak. The increasingA-site disorder characterized by variance of ␴² results in the fol- lowing effects: 共i兲 the ferromagnetic transition temperature and magnetization of the samples decrease significantly;共ii兲 an irreversibility between the ZFC and FC magnetizations against temperature appears and the system transforms from ferromagnetic state to cluster glass-state;共iii兲an abrupt MIT of the ground state is confirmed and a good ln␳⬃T^1/4rela- tionship共VRH兲for the high-disordered samples is observed;

共iv兲theM-Hcurves of the sample with intermediate disorder 共␴²= 0.008兲 exhibit a sharp stepwise behavior at a field H

⬃3.5 T.

A phase separation scenario is used to explain these ex- perimental effects. With increasing A-site disorder, the ran- dom oxygen displacements and then random local radial dis- tortions of the MnO₆ octahedra become significant and the Mn-O-Mn bond angle becomes smaller. TheA-site disorder brings about the electron localization that burdens the Mn- O-Mn double-exchange interaction mediated by the conduc- FIG. 10. Inverse susceptibility 1 /␹ as a function of T for the

samples with共a兲␴²= 0.0003 and共b兲␴²= 0.007 measured underH

= 100 Oe. The dashed lines are the fitting results following the Curie-Weiss law. The unit of␴²is Ų.

tion electrons. The long-range FM ground state at ␴²

⬍0.007 loses its dominance to the short-range magnetically ordered state as␴²⬎0.008. The disorder and the competing interactions are responsible for the occurrence of spin clus- ters, and the weak magnetic interaction between these clus- ters leads to the cluster-glass-like behavior.

ACKNOWLEDGMENTS

This work was cosupported by the Natural Science Foun- dation of China 共50332020, 10021001, 50528203兲 and Na- tional Key Projects for Basic Research of China 共2002CB613303, 2004CB619004兲.

*Author to whom correspondence should be addressed. Email ad- dress: [email protected]

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